float CalcBox(Face *f, Point3 *v, Line *Lc, UG *G,
IntPoint3 *vn, IntPoint3 *vp, float Radius)
{
Point3 BoxCenter;
float FaceRadius;
float offset;
FaceRadius=V3DistanceBetween2Points(&(Lc->Lu), &(v[f->v[0]]));
offset=sqrt(Radius*Radius - FaceRadius*FaceRadius);
BoxCenter.x=Lc->Lu.x+Lc->Lv.x*offset;
BoxCenter.y=Lc->Lu.y+Lc->Lv.y*offset;
BoxCenter.z=Lc->Lu.z+Lc->Lv.z*offset;
vn->x = (int)((BoxCenter.x - G->vn.x - Radius)/G->side);
vn->y = (int)((BoxCenter.y - G->vn.y - Radius)/G->side);
vn->z = (int)((BoxCenter.z - G->vn.z - Radius)/G->side);
vp->x = (int)((BoxCenter.x - G->vn.x + Radius)/G->side);
vp->y = (int)((BoxCenter.y - G->vn.y + Radius)/G->side);
vp->z = (int)((BoxCenter.z - G->vn.z + Radius)/G->side);
vn->x=max(0,vn->x);
vn->y=max(0,vn->y);
vn->z=max(0,vn->z);
vp->x=min(G->x-1,vp->x);
vp->y=min(G->y-1,vp->y);
vp->z=min(G->z-1,vp->z);
return(Radius*Radius);
}
Tetra *MakeTetra(Face *f,Point3 *v[], int n)
{
Plane p,Mp;
boolean found=FALSE;
double Radius=BIGNUMBER, rad;
Line Lc;
int pind=0;
Tetra *t;
Point3 Center, c;
int i;
if(!CalcPlane(f->v[0],f->v[1],f->v[2],&p))
Error("MakeTetra, Face with collinar vertices!\n",EXIT);
CalcLineofCenter(f->v[0],f->v[1],f->v[2],&Lc);
for(i=0;i<n;i++)
{
if((v[i]!=f->v[0]) &&
(v[i]!=f->v[1]) &&
(v[i]!=f->v[2]) &&
RightSide(&p,v[i]) )
{
CalcMiddlePlane(v[i],f->v[0],&Mp);
if(CalcLinePlaneInter(&Lc,&Mp,&c))
{
rad=V3SquaredDistanceBetween2Points(&c, v[i]);
if(!RightSide(&p,&c)) rad=-rad;
if(rad==Radius) Error("MakeTetra, Five cocircular points!\n",EXIT);
if(rad<Radius)
{
found=TRUE;
Radius=rad;
Center=c;
pind=i;
}
}
}
}
if(!found) return NULL;
t=BuildTetra(f,v[pind]);
if(CheckFlag) CheckTetra(t,v,n);
if(StatFlag)
{Point3 C;
CalcSphereCenter(f->v[0], f->v[1], f->v[2], v[pind], &C);
SI.Radius+=V3DistanceBetween2Points(&C, v[pind]);
}
return t;
}
void CheckTetra(Tetra *t, Point3 *v[], int n)
{
int i;
Point3 Center;
double Radius;
double d;
if(!CalcSphereCenter(t->f[0]->v[0],
t->f[0]->v[1],
t->f[0]->v[2],
t->f[1]->v[1], &Center ))
Error("CheckTetra, Bad Tetrahedron, CalcSphereCenter Failed!\n",EXIT);
Radius = V3DistanceBetween2Points(&Center, t->f[0]->v[0]);
for(i=0;i<n;i++)
{
d=V3DistanceBetween2Points(&Center,v[i]);
if( d < Radius - EPSILON)
Error("CheckTetra, A not Delaunay Tetrahedron was built!\n",EXIT);
}
}
Tetra *FirstTetra(Point3 *v[], int n)
{
int i, MinIndex=0;
double Radius, MinRadius=BIGNUMBER;
Tetra *t;
Plane p[3], Mp;
Line Lc;
Face f;
Point3 c;
boolean found=FALSE;
f.v[0]=v[n/2-1]; /* The first point of the face is the */
/* nearest to middle plane in negative */
/* halfspace. */
/* The 2nd point of the face is the */
/* euclidean nearest to first point */
for(i=n/2;i<n;i++) /* that is in the positive halfspace */
{
Radius=V3SquaredDistanceBetween2Points(f.v[0], v[i]);
if(Radius<MinRadius)
{
MinRadius=Radius;
MinIndex=i;
}
}
f.v[1]=v[MinIndex];
/* The 3rd point is that with previous */
/* ones builds the smallest circle. */
CalcMiddlePlane(f.v[0],f.v[1], &(p[0]));
MinRadius=BIGNUMBER;
for(i=0;i<n;i++)
if(v[i]!=f.v[0] && v[i]!=f.v[1])
{
CalcMiddlePlane(f.v[0], v[i],&(p[1]));
if(CalcPlane(f.v[0],f.v[1],v[i],&(p[2])))
if(CalcPlaneInter(&(p[0]), &(p[1]), &(p[2]), &c))
{
Radius=V3DistanceBetween2Points(&c, f.v[0]);
if(Radius<MinRadius)
{
MinRadius=Radius;
MinIndex=i;
}
}
}
f.v[2]=v[MinIndex];
/* The first tetrahedron construction is analogous to normal */
/* MakeTetra, only we dont limit search to an halfspace. */
MinRadius=BIGNUMBER;
CalcPlane(f.v[0], f.v[1], f.v[2],&p[0]);
CalcLineofCenter(f.v[0], f.v[1], f.v[2], &Lc);
for(i=0;i<n;i++)
if(v[i]!=f.v[0] && v[i]!=f.v[1] && v[i]!=f.v[2] )
{
CalcMiddlePlane(v[i], f.v[0], &Mp);
if(CalcLinePlaneInter(&Lc, &Mp, &c))
{
Radius=V3SquaredDistanceBetween2Points(&c, v[i]);
if(MinRadius==Radius) Error("FirstTetra, Five cocircular points!\n",EXIT);
if(Radius<MinRadius)
{
found=TRUE;
MinRadius=Radius;
MinIndex=i;
}
}
}
if(!found) Error("FirstTetra, Planar dataset, unable to build first tetrahedron.\n",EXIT);
if(!RightSide(&p[0],v[MinIndex])) ReverseFace(&f);
t=BuildTetra(&f, v[MinIndex]);
CheckTetra(t,v,n);
ReverseFace(t->f[0]); /* First Face in first Tetra */
/* must be outward oriented */
return t;
}
Tetra *FastMakeTetra(Face *f, Point3 *v, int n, UG *G)
{
Plane p;
Tetra *t;
float CellBoxRadius= 0.0, /* Radius of Cell Box to scan for dd-nearest */
BoxRadius,
FaceRadius,
MinRadius=BIGNUMBER;
struct argGroup args;
Line Lc;
IntPoint3 vn,vp, start, end, inc;
int Index=-1;
boolean Found=FALSE;
SI.MakeTetra++;
UGResetMark(G);
if(!CalcPlane(&(v[f->v[0]]),&(v[f->v[1]]),&(v[f->v[2]]),&p))
Error("Faccia composta da tre punti allineati!!\n",EXIT);
CalcLineofCenter(&(v[f->v[0]]),&(v[f->v[1]]),&(v[f->v[2]]),&Lc);
FaceRadius=V3DistanceBetween2Points(&(Lc.Lu), &(v[f->v[0]]));
args.f = f;
args.Lc = &Lc;
args.p = &p;
args.G = G;
// printf("checkpoint 0\n");
do
{
CellBoxRadius++;
BoxRadius=CalcBox(f,v,&Lc,G,&vn,&vp, CellBoxRadius*FaceRadius);
Found=ScanCellBox(&vn, &vp, v,&args,&Index, &MinRadius);
}
while(!Found && CellBoxRadius <= 1);
//printf("checkpoint 1\n");
// printf("MinRadius = %f BoxRadius = %f\n",MinRadius, BoxRadius);
if(Found && MinRadius>BoxRadius)
{float oldMinRadius=MinRadius;
SI.SecondBox++;
// printf("f->v[0] = %d, f->v[1] = %d, f->v[2] = %d, sqrt(MinRadius) = %f\n",f->v[0],f->v[1],f->v[2], sqrt(MinRadius));
BoxRadius=CalcBox(f,v,&Lc,G,&vn,&vp, sqrt(MinRadius));
// printf("checkpoint 2\n");
//printf("vn->x = %d ,vn->y = %d, vn->z = %d, vp->x = %d, vp->y = %d, vp->z = %d, radius = %f\n",vn.x, vn.y, vn.z, vp.x, vp.y,vp.z,MinRadius);
ScanCellBox(&vn, &vp, v, &args, &Index, &MinRadius);
//printf("checkpoint 2.1\n");
if(oldMinRadius>MinRadius) SI.UsefulSecondBox++;
}
if(!Found)
{
//printf("checkpoint 3\n");
SI.EmptyBox++;
CalcLastScan(G, &start, &end, &inc, &p);
//printf("checkpoint 4\n");
Found=MakeLastScan(&start, &end, &inc, v, &args, &Index,&MinRadius);
}
//printf("chekpoint 5\n");
if(!Found) return NULL;
if(MinRadius>0)
{
SI.MinRadius+=sqrt(MinRadius);
SI.MinRadiusNum++;
}
t=BuildTetra(f,Index);
if(StatFlag)
{Point3 C;
CalcSphereCenter(&(v[f->v[0]]),&(v[f->v[1]]),&(v[f->v[2]]),&(v[Index]),&C);
SI.Radius+=V3DistanceBetween2Points(&C, &(v[Index]));
}
if(CheckFlag) CheckTetra(t,v,n);
return t;
}